1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2022/2023
4. Mathematics - pierwszego stopnia z tyt. licencjata
5. Modeling in Finance

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Modeling in Finance - opis przedmiotu

Cel przedmiotu

The subject covers issues related to the use of selected mathematical modeling methods in finance and insurance.
The aim of the classes is to become familiar with the basic modeling methods in financial markets and insurance and their practical use.

Wymagania wstępne

Zapisz zmiany

Knowledge of basic courses in mathematical analysis, probability theory, mathematical statistics, basics of financial mathematics, financial engineering, differential equations, numerical methods.

Zakres tematyczny

Lectures:
1. Mathematical modeling – essence, scope, stages; types and construction of mathematical models.
2. Methods used in modeling: least squares method, divided differences, splines, computer fits
3. “Tools” used in finance: accumulation processes, term structures of interest rates, financial contracts, debt repayment plans, forward rates of return.
4. Valuation of financial instruments: present and future value, internal rate of return.
5. Actuarial mathematics – application: redemption funds, depreciation.
6. Financial market and stock exchanges: single price, basic and derivative instruments - valuation.
7. Pricing of European options – Black-Scholes model.
8. Exotic options – methods of their valuation.
9. Stochastic methods in investing: microeconomic approach to investment strategies, Markowitz model, two- and multi-component portfolios, Value at Risk - investment protection.

Laboratory:
1. Modeling forward interest rates using various types of term structures.
2. Modeling loan repayment plans using various methods.
3. Modeling of investment projects - using the internal rate of return and other profitability measures to select an appropriate investment strategy.
4. Modeling of depreciation schemes for selected investment cases.
5. Valuation of basic and derivative instruments and computer simulation of results in discrete and continuous financial models.
6. Investment strategies in a stochastic approach - illustration and computer simulation of selected stochastic investment methods.

Metody kształcenia

Lecture:
The issues discussed in a classic way are illustrated with accounting examples. Additionally, each issue is accompanied by tasks to be solved on your own.

Laboratory:
Solving (in a team and individually) tasks with real data using available computer packages. Each task is preceded by a discussion about the necessary theoretical tools and how to use them. Reports on the use of the discussed theoretical and practical methods are prepared for the proposed solutions.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

Laboratory:
Tests during classes examining the practical use of knowledge acquired during lectures and previously completed courses (e.g. statistics, probability theory, numerical methods, etc.). In addition, activity in classes and assessment of group cooperation in order to solve given problems.

Lecture:
Written exam in the practical application of methods learned during the lecture. The scope of the exam corresponds to the scope of practical tasks added to the topics discussed in the lecture.

The course grade consists of the laboratory grade (40%) and the exam grade (60%).

The condition for taking the exam is a positive grade from the laboratory.

The condition for passing the course is a positive grade in the laboratory and exam.

Literatura podstawowa

1. J.C. Hull, Options, Futures and other Derivatives - Tenth edition, Pearson Education, New York, 2018.
2. S. Blyth, An Introduction to Quantitative Finance, Oxford University Press, Oxford, 2014.
3. H.D. Junghenn, An Introduction to Financial Mathematics. Option Valuation. Second Edition, CHAPMAN & HALL/CRC Press Taylor & Francis Group, Boca Raton London New York, 2019.
4. A.O. Petters, X. Dong, An Introduction to Mathematical Finance with Applications. Understanding and Building Financial Intuition, Springer, 2016.
5. C.H. Skiadas (ed.), Recent Advances in Stochastic Modeling and Data Analysis, World Scientific Publishing Co. Pte. Ltd., Singapore, 2007.

Literatura uzupełniająca

1. S.R. Pliska, Introduction to Mathematical Finance. Discrete Time Models, Blackwell Publishers Ltd., Oxford, 2001.
2. P.L. Anderson, Business Economics and Finance with MATLAB, GIS and Simulation Models, CHAPMAN & HALL/CRC Press LLC, Boca Raton London New York Washington, D.C., 2005.
3. P. Brandimarte, Numerical Methods in Finance and Econometrics. A MATLAB Based Introduction, 2nd ed., John Wiley & Sons, Inc., Hoboken, New Jersey, 2006.
4. A.N. Shiryaev, Essentials of Stochastic Finance, Facts, Models, Theory, World Scientific, 1999.

Uwagi

Zmodyfikowane przez dr Joachim Syga (ostatnia modyfikacja: 03-03-2024 22:57)